Answer:
1. The possible roots are ±1, ±2, ±3, ±6. These are the factors of the trailing constant (6) divided by the factors of the leading coefficient (1). When the leading coefficient is 1, the possible roots are the factors of the constant
2. The polynomial is easier to evaluate when it is written in Horner form:
f(x) = ((x -4)x +1)x +6
To show that 2 is a zero, we want to find f(2):
f(2) = ((2 -4)2 +1)2 +6 = (-4 +1)2 +6 = -6 +6 = 0
f(2) = 0, so 2 is one of the zeros of this function
3. Using synthetic division (attached) or polynomial long division, we can divide the given polynomial by (x-2) to find the remaining factors. This division gives (x^2 -2x -3), which can be factored as (x -3)(x +1), so the three actual roots are ...
x = 2 (from above), x = 3, x = -1 (from our factorization)
4. In factored form, the polynomial can be written ...
f(x) = (x +1)(x -2)(x -3)
The first factor was found from the fact that 2 was given as a zero of the function. For any zero "a", a factor of the polynomial is (x-a).
The remaining factors were found by factoring the quadratic trinomial that resulted from the division of f(x) by x-2. That trinomial is x^2 -2x -3.
There are a number of methods that can be used to factor x^2 -2x -3. Again, the rational root theorem can help. It suggests that ±1 and ±3 are possible roots.
6. Three cards are drawn from an ordinary deck and not replaced. What is the
probability of getting 3 spades?
We want to find the probability of randomly drawing 3 spades from a standard deck.
The probability of getting 3 spades is 0.0129
Let's see how to get that probability.
A standard deck has 52 cards, 13 of them are spades.
The probability of randomly drawing a spade card is given by the quotient between the number of spades and the total number of cards.
So for the first spade card, the probability is:
p = 13/52
For the second card, take in mind that we already drew a spade card, so now there are 12 spade cards and 51 cards in total, so we have:
q = 12/51
For the final card, there will be 11 spade cards and 50 cards in total, but we will have:
k = 11/50
The joint probability (this is, the probability of getting the 3 spade cards one after the other) is equal to the product of the individual probabilities, so we will get:
P = p*k*q = (13/52)*(12/51)*(11/50) = 0.0129
The probability of getting 3 spades is 0.0129
If you want to learn more, you can read:
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Plz help I need help
Answer:
What do you need help with mate?
Step-by-step explanation:
you don't have a question posted.
Find the volume of the prism.
3 cm
37 cm
5 cm
A number that has more than two factors is a
Composite number? I’m not sure if that’s what you’re working on but it’s a true statement.
correct answers Please!!
Answer:
114 miles
Step-by-step explanation:
A scuba diver is descending at an average rate of 39.8 feet per minute.
What value represents the scuba diver's elevation relative to sea level after 2.9 minutes?
Enter your answer in the box.
ft
Plzzzz help I will give u brainly
Answer: 115.42 ft
Step-by-step explanation:
if buyer purchases 25% of a lot in the spring and then purchases 50% more in the fall what percentage of the lot is still available to purchase
Answer:
25%
Step-by-step explanation:
Total purchase = 25%+50%
Total purchase = 75%
Percentage left = 100% - 75%
Percentage left = 25%
Henry draws triangle FGH. Then, he translates that triangle to create triangle F'G'H'. The distance from F to F' is 4 centimeters. What is the length of sides GG'? a. 2 cm b. 3 cm c. 4 cm d. 6 cm
The length of sides GG' when the distance from FF' is 4 cm is also 4 cm.
A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.
When you perform translations, you slide a figure left or right, up or down. This means that, in the coordinate plane, the coordinates for the vertices of the figure will change.
It is given that Henry translates the ΔFGH to create ΔF'G'H'.
FF' = 4cm.
Translation is a rigid transformation. In translation, every point of the object must be moved by same distance and in the same direction.
In other words the distance between corresponding points are same.
GG' =?
Since G and G' are corresponding points, so
GG' = FF'
GG' = 4 cm
The length of GG' is 4 centimeters.
Hence, When the distance from FF' is 4 cm, the length of sides GG' is similarly 4 cm. so option C is the correct answer.
To learn more about Translation
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Select the better deal in the pair. Then give the unit rate for the better deal.
$182/7g
or
$342/9g
Answer:182/7g
Step-by-step explanation: 182 divide by 7= 26
342 divide by 9=38
and you want the lowest cost so a.
When converted to a household measurement, 9 kilograms is approximately equal to a
What is 317.466 ounces or 19.8 pounds
1kg in household measurement is equal to 35.274 ounces.
So, 35.274*9= 317.466 ounces
317.466/16= 19.8 pounds
Please allow me to know this helped with brainly.
Thank you - Miss Hawaii
Answer:
D) 19.8 lbs
Explanation:
1kg in household measurement is equal to 35.274 ounces. 35.274*9=317.466 ounces.
1kg is also equal to 2.205 lbs. 9*2.205=19.8416
9 kg is also equal to 9000 grams, but grams are not a part of the household measurement system
a) 9000 grams. b) 9000 ounces. c) 19.8 ounces. d) 19.8 pounds.
This leaves us with 19.8 lbs
the equation for the vertical line that goes through point V (−5, 17).
Answer:
The answer to the above question is x = -5
What percent of the hours were billed by Jon, Roy, or Dean?
Write your answer using a percent
sign (%).
Answer:
10%
Step-by-step explanation:
please tell me if im right or wrong
Find the length of the shorter leg of a right triangle if the longer leg is 11 feet more than the shorter leg and the hypotenuse is 11 feet less than twice the shorter leg.
Step-by-step explanation:
of a right triangle if the longer leg is 11 feet more than the shorter leg and the hypotenuse is 11 feet less than twice the shorter leg.
Write the place value of underlined digit in 8.745
Answer:
thousandths I'm pretty sure
code for the below question
We have to calculate the area of a rectangle, a square and a circle. Create an
interface 'Shape' with three methods declarations namely 'RectangleArea' taking two
parameters, 'SquareArea' and 'CircleArea' taking one parameter each. The parameters
of 'RectangleArea' are its length and breadth, that of 'SquareArea' is its side and that of
'CircleArea' is its radius. Now create another class 'Area' containing all the three
methods 'RectangleArea', 'SquareArea' and 'CircleArea' for printing the area of
rectangle, square and circle respectively. Create an object of class 'Area' and call all the
three methods.
Step-by-step explanation:
can I use python?
yes or no
Please help me on this thank you I’ll give brainliest
Answer:
Eh, you're not getting any help since you lied about "giving brainliest".
Step-by-step explanation:
pls help i am in k12
What is the slope of Car A’s graph? What does it mean?
(b) What is the slope of Car B’s table? What does it mean?
PLEASE HURRY!! WILL GIVE BRAINLIEST
In the space below, use the law of sines or trigonometric ratios to find each length. Round your answer to 1 decimal place. (4 points total: 1 point each)
a. The length of the zip line, z
b. The height of the point on the tree where the top of the ladder rests against it, h
c. The distance between the base of the ladder and the base of the tree, b
d. The distance between the base of the tree and the spot where the zip line is anchored to the ground, B
Trigonometric ratios are useful in calculating the side lengths of a triangle.
The length of the zip line is 222.5 ftThe height where the ladder rests against the tree is 38.6 ftThe distance between the base of the ladder and that of the tree is 10.4 ftThe distance between the base of the tree and the spot where the zip line is anchored to the ground is 219.1 ft(a) Length, z
First we calculate (h) using the following sine ratio
[tex]\mathbf{sin(75) = \frac{h}{40}}[/tex]
Make h the subject
[tex]\mathbf{h = 40sin(75)}[/tex]
Next, we calculate (z) using the following sine ratio
[tex]\mathbf{sin(10)= \frac{h}{z}}[/tex]
Make z the subject
[tex]\mathbf{z= \frac{h}{sin(10)}}[/tex]
Substitute [tex]\mathbf{h = 40sin(75)}[/tex]
[tex]\mathbf{z= \frac{40sin(75)}{sin(10)}}[/tex]
[tex]\mathbf{z= 222.5 ft}[/tex]
Hence, the length of the zip line is 222.5 ft
(b) The height, h
In (a), we have
[tex]\mathbf{h = 40sin(75)}[/tex]
Evaluate
[tex]\mathbf{h = 38.6}[/tex]
Hence, the height where the ladder rests against the tree is 38.6 ft
(c) The distance, b
To do this, we make use of the following sine ratio
[tex]\mathbf{sin(15) = \frac{b}{40}}[/tex]
Make b the subject
[tex]\mathbf{b = 40sin(15)}[/tex]
[tex]\mathbf{b = 10.4}[/tex]
Hence, the distance between the base of the ladder and that of the tree is 10.4 ft
(d) Distance, B
To do this, we make use of the following sine ratio
[tex]\mathbf{sin(80) = \frac{B}{z}}[/tex]
Make B the subject
[tex]\mathbf{B = z\ sin(80)}[/tex]
Substitute [tex]\mathbf{z= 222.5 ft}[/tex]
[tex]\mathbf{B = 222.5\ sin(80)}[/tex]
[tex]\mathbf{B = 219.1}[/tex]
Hence, the distance between the base of the tree and the spot where the zip line is anchored to the ground is 219.1 ft
Read more about trigonometry ratios at:
https://brainly.com/question/24888715
Write the recurring decimal 0.05 as a fraction in its simplest form
Answer:
1/20
Step-by-step explanation:
Step 1: Write the given number as the numerator and place 1 in the denominator right below the decimal point followed by the number of zeros required accordingly.
In this case, 0.05 has two numbers after the decimal, so, we place 100 in the denominator and remove the decimal point. This will make it 5/100
Step 2: Then, this fraction can be simplified. 5/100 = 1/20
Thus, 0.05 as a fraction is written as 1/20
Answer:
Step-by-step explanation:
let the fraction be a
a*100.....=0.05*100
100a......=05.00
99a....=0.05
100a= 5.00
99a= 0.05
a= 4.95/99
Two angles in a triangle are have the same measurement. The third angle is 12 degrees less than
the first angle. What are the measurements of angle 1, 2 and 3? (hint: you will need to know
how many degrees are in an triangle)
HELP HURRY SUBTRACTION
Answer:
408, 250, and 4055 hope this helps
5
2
m−
5
4
−
5
3
m
Answer:
(Hope this helps can I pls have brainlist (crown)☺️)
Step-by-step explanation:
In pic
(Credits: Symbolab)
(Hope this helps can I pls have brainlist (crown)☺️)
A dozen large muffins cost $7.99.
How much does each muffin cost?
Answer:
1.501877347
Step-by-step explanation:
estamate or whaever u need to do
For each team, find the unit rate games per loss.
Answer:
Ой ну не знаю очень сложный вопрос
Find the difference.
678-595.8
Answer:
82.2
Step-by-step explanation:
The difference is subtracting:
678 - 595.8 = 82.2
Answer:
82.2
Step-by-step explanation:
Check the image below.
Simplify t^12/t^6
A. 2
B. 6
C. 6
D. 7-2
Answer:
t
12
/t
6
=t
12−6
=t
6
if this helps your welcome
1 1
11
yly
УУ УУ
Part A
? Question
Create an equation from the model that describes the relationship between the weights on each side of the scale
Enter the correct answer in the box.
0 0 0
OP
α β
sin cos tan sin cos tan!
0
2 Δ Ο
Σ
0
X
A
9514 1404 393
Answer:
2y +3 = 4y +2
Step-by-step explanation:
The left side shows 2y +3.
The right side shows 4y +2.
The scale is shown in balance, so we must have ...
2y +3 = 4y +2 . . . . equation from the model
__
The solution can be found by subtracting 2y+2 from both sides to leave ...
1 = 2y
Then we can divide both sides by 2 to find what y stands for:
1/2 = y . . . . solution to the equation
solve for completing the square x^2-12x+11=0
Answer:
x = 6 ± 5
Step-by-step explanation:
x² - 12x + 11 =0
x² - 12x = -11 Now add this number to both sides of the equal sign (1/2 of the coefficient of x-term squared)
x² - 12x +36 = -11 + 36 1/2(-12)² = 36
(x - 6)(x - 6) = 25
(x - 6)² = 25
[tex]\sqrt{(x-6)}[/tex]² = [tex]\sqrt{25}[/tex] square root of both side of the equation
x - 6 = ± 5 (5)² = 25 and (-5)² = 25
x = 6 ± 5
Dan received these tips in a given week. How much were his total tips.?
Answer:
we need the amount of tips to answer this ;-;
Step-by-step explanation:
Paloma evaluated the expression 1 3/4 − 5/8. What is a way she can check her work?
9514 1404 393
Answer:
add the subtrahend to the difference
Step-by-step explanation:
The usual way to check a subtraction problem is to add the subtrahend to the difference to see if you get the minuend as a result.
Paloma can add 5/8 to her result to see if she gets 1 3/4.
__
She can also perform the subtraction using decimal fractions to see if she gets the same result.
1.750 -0.625 = 1.125